Function normalizeIndexingSet

src/compute-engine/library/utils.ts:136–187

(indexingSet: Expression)

 *
 * A component that is not provably numeric at all — a matrix ROW, a string, an
 * `unknown`-typed element — keeps `number` too, ahead of both: those have no
 * norm for this claim to be about.
 *
 * `real` is the claim for every other component set, complex components
 * included. No narrower tier is: unlike `|·|` of a scalar, a norm does not
 * preserve the integer or rational tier — `‖(1, 1)‖ = √2`.
 */
export function euclideanNormType(
  components: ReadonlyArray<OperandDescriptor>
): string {
  if (components.length === 0) return 'number';
  if (!components.every((c) => isSubtype(c.type, 'number'))) return 'number';
  if (
    components.every(
      (c) => c.facts.finite === true || isSubtype(c.type, 'complex')
    )
  )
    return 'real';
  if (components.every((c) => isSubtype(c.type, EXTENDED_REAL_TYPE)))
    return 'real | +oo';
  return 'number';
}

/**
 * Result type of the Euclidean norm of a fixed-arity point (`Tuple` operand of
 * `Norm`/`Abs`): the scalar norm type, unless the point broadcasts. Only a
 * point whose components the structural view exposes carries the scalar
 * claim; a point-TYPED symbol keeps the wide `number`.
 */
export function pointNormType(d: OperandDescriptor): string {
  if (pointNormBroadcasts(d)) return 'list<number>';
  const children = operandChildren(d);
  if (children === undefined) return 'number';
  return euclideanNormType(children);
}

/**
 * EL-4: Convert known infinite integer sets to their equivalent Limits bounds.
 * Returns undefined if the set cannot be converted to a Limits form.
 *
 * Mappings:
 * - NonNegativeIntegers (ℕ₀) → [0, ∞)
 * - PositiveIntegers (ℤ⁺) → [1, ∞)
 * - NegativeIntegers (ℤ⁻) → Not supported (would need negative direction)
 * - Integers (ℤ) → Not supported (bidirectional)
 * - Other sets (Reals, Complexes, etc.) → Not supported (non-integer)
 */
export function convertInfiniteSetToLimits(
  domainSymbol: string
): { lower: number; upper: number; isFinite: false } | undefined {
  switch (domainSymbol) {
    case 'NonNegativeIntegers':
      // ℕ₀ = {0, 1, 2, 3, ...}
      return { lower: 0, upper: MAX_ITERATION, isFinite: false };
    case 'PositiveIntegers':